Ruling engine for generating dies to mold anamorphic fresnel optics

ABSTRACT

An improvement for a ruling engine enables the ruling engine to generate master dies for molding Fresnel optics with a cylindrical or a toroidal power component together with a spherical power component and thereby implement a method for generating anamorphic Fresnel optical elements. The improvement includes a device to change the pitch of the ruling engine&#39;&#39;s cutting tool as a function of its azimuth on a work piece revolving beneath it.

United States Patent 1191 Plummer Mar. 25, 1975 [75] Inventor: William T. Plummer, Concord,

Mass.

[73] Assignee: Polaroid Corporation, Cambridge,

Mass.

[22] Filed: Jan. 2, 1973 [21] App]. No.: 320,611

[52] US. Cl. 82/12, 82/19 [51] Int. Cl 1 I@3/28 [58] Field of Search....; 82/11, l2, 18, 19

[56] References Cited UNITED STATES PATENTS 1,803,429 5/1931 Gunning 82/12 3,079,731 3/1963 Rawstron et a1.... 82/12 X" 3,128,657 4/1964 Hebert 82/19 X RULING ENGINE FOR GENERATING DIES TO MOLD ANAMORPHIC FRESNEL OPTICS 3,135,148 6/1964 Cole et al7 82/12 X 3,221,577- 12/1965 Baum 82/12 3,490,336 1/1970 Staub 82/18 X 3,626,456 12/1971 Freeborn 3,688,611 9/1972 Neuman..... 3,744,357 7/1973 Anderson 82/12 Primary Examinerl-larrison L. Hinson Attorney, Agent, or Firm-Frederick H. Brustman; John W. Ericson [57] ABSTRACT An improvement for a ruling engine enables the ruling engine to generate master dies for molding Fresnel optics with a cylindrical or a toroidal power component together with a spherical power component and thereby implement a method for generating anamorphic Fresnel optical elements. The improvement includes a device to change the pitch of the ruling engines cutting tool as a function of its azimuth on a work piece revolving beneath it.

7 Claims, 7 Drawing Figures SEYZW'MS PfJENTEU m2 5 i975 SHEET 3 OF 6 PATENTED 51975 SHEET a 0? 6 FIG.3

PATENTEB IW25 I975 $872. 749

sum 5 a g- FIG. 4

RULING ENGINE FOR GENERATING DIES TO MOLD ANAMORPHIC FRESNEL OPTICS BACKGROUND OF THE INVENTION In my earlier and copending patent application Ser. No. 141,253, filed May 7, 1971, and assigned to Polaroid Corporation (now U.S. Pat. No. 3,735,685), 1 disclosed a novel focusing screen. The novel focusing screen forms stigmatic images of remote conjugate. points by reflection. It includes a generally planar surface with a special Fresnel mirror composed of a plurality of successively larger concentric ellipsoidal segments. Each ellipsoidal segment conforms to the shape of an ellipsoid having the conjugate points as foci at the locus of intersection of the planar surface and the ellipsoid. Clearly, each ellipsoidal segment will reflect light impinging on it from one foci or point to the conjugate foci or point. All the segments will coact to do the same. Thus, my special Fresnel mirror will operate as a condensing optic to image an entrance pupil, centered about one foci or point, at an exit pupil, centered about the other foci or conjugate point. The image is substantially stigmatic because the special Fresnel mirror is essentially anamorphic.

A less expensive but still satisfactory variant of the stigmatic Fresnel mirror is also disclosed in the aforementioned said U.S. Pat. No. 3,735,685. The variant Fresnel mirror comprises a plurality of of that are circular rather than ellipsoidal in the plane of the surface. The face of each circular echelon is reflective and the slope of a face at any point on the surface of the Fresnel mirror variant is substantially equal to the slope otherwise obtained from an ellipsoidal segment at that point.

Previous Fresnel optical elements each comprise, on a planar surface, a plurality of circular grooves concentric about the axis of the optic. Each circular groove on a Fresnel optical has a smooth facet with a pitch approximately tangent to the surface of a conventional optical element of similar optical power at a radius from the optical axis equal to the radius of the groove. Thus, on a positive Fresnel lens, the pitch of each grooves facet increases with its radial distance from the optical axis of the Fresnel lens. It is known to correct Fresnel optics for spherical aberrations by imparting to the facets further from the axis a pitch calculated to effect that correction. However, in all cases the grooves and their facets are, nevertheless, still symmetric about the optical axis of the Fresnel optic. This results in a Fresnel optic with the same power in all azimuths.

An essential element of novel Fresnel optics like those of my said U.S. Pat. No. 3,735,685 is different powers in different azimuths. In particular, the power should be a maximum in one azimuth and a minimum in the orthogonal azimuth as in a conventional spectacle lens having both spherical and cylindrical components of power.

Such anamorphic Fresnel optics have grooves wherein the facet will have a maximum pitch at two azimuths 180 degrees apart and a minimum pitch at azimuths 90 degrees from those points with the pitch decreasing between. These grooves or echelons can be considered anamorphic-shaped grooves.

Ruling engines for generating master dies for molding Fresnel lenses and Fresnel mirrors of the type known previous to my disclosure in said U.S. Pat. No. 3,735,685 are limited to ruling a circular echelon with a face having a constant slope or pitch with respect to the axis of the Fresnel lens or mirror. That is, the slope remains the same at all azimuths around the circular echelon (ruling). Therefore, a Fresnel mirror molded from a master generated by any previously known ruling engine or by any previously known technique would impart an unacceptable amount of astigmatism in the image of a point it formed at a remote point.

SUMMARY OF THE INVENTION The present invention contemplates a novel method for generating a master die for molding anamorphic Fresnel optics as well as a novel ruling engine and a novel improvement for an existing ruling engine enabling them to generate dies for anamorphic Fresnel mirrors and lenses according to that method.

The method for generating anamorphic Fresnel master dies for molding optics adds to the conventional method for generating Fresnel dies the novel step of changing the pitch of the cutting tool as a function of its azimuth on the anamorphic Fresnel die being ruled. Generally, the method calls for the pitch to increase to a maximum at two points around a circular echelon groove separated by 180 and to decrease to a mini mum at two other points around the circular echelon groove. Each minimum point is separated by from the maximum points. Usually, the method is carried out so the pitch will decrease uniformly from its maximum to its minimum and increase uniformly from its minimum to its maximum so the resultant Fresnel die possesses bi-fold symmetry.

The inventive improvement disclosed in this application is also a means for changing the pitch of an echelon cutting tool between a maximum value and a mini mum value as a function of the tools azimuth on a rotating work piece. Additionally, the means includes the ability to change the difference between the tools maximum pitch and its minimum pitch as a function of the tools radial distance from the rotational center of the work piece.

Accordingly, it is an object of the present invention to provide a novel method to make a master die for molding anamorphic Fresnel optical elements.

Another object of the present invention is to provide a means for carrying out, in a convenient manner, the novel method disclosed herein.

Yet another object of the present invention is an improvement for a ruling engine to enable it to generate master dies for molding anamorphic Fresnel optical elements.

DESCRIPTION OF THE DRAWINGS Other objects and many of the attendant advantages of the present invention will be better appreciated and said invention will become clearly understood by reference to the following detailed description when considered in conjunction with the accompanying drawings illustrating a ruling engine embodying the present invention, wherein:

FIG. 1 illustrates, partially in section, an improved ruling engine with means for varying its cutting tool's pitch as a function of radius and azimuth with respect to a work piece;

FIG. 2 illustrates in greater detail the structure supporting the ruling engines cutting tool;

FIG. 2a illustrates an arcuate bearing permitting the cutting tool to rotate about a point along its edge;

FIG. 3 illustrates in detail a cam operating mechanism shown generally in FIG. 1;

FIG. 4 illustrates the ruling engine in plan view; and

FIGS. 5a and 5b illustrate, respectively, a conventional Fresnel optic and an anamorphic Fresnel optic.

THE PREFERRED EMBODIMENT A ruling engine embodying my inventive concept for a means to generate master dies for molding a Fresnel optical element with anamorphic rulings is shown,

partially in section, in FIG. 1. It also appears in a plan view in FIG. 4. Reference should be had to both FIGS. figures.

The ruling engine 10 comprises four principal operating mechanisms supported on a suitably rigid frame 12: a revolving turntable 14 to hold a work piece 16 and to turn it about a center or rotation; a cutting head 18 for positioning a cutting tool or ruling stylus 20 at a selected radius from the center of rotation and for controlling the depth to which the cutting tool 20 will groove the work piece 16; a pitch control mechanism 22 for adjusting the pitch of the cutting tool 20 as a function of the cutting tool 20s radial distance from the center of rotation and as a function of the cutting tool 20s azimuth on the work piece 16 as the latter revolves; and a transmission 24 for rotating a cam 26, on the pitch control mechanism 22, synchronously with the revolving turntable l4 regardless of the longitudinal position or elevation of the cam 26.

The turntable 14 is rigidly attached to a turntable axle 28. Its upper surface rotates in a plane normal to the axis of the turntable axle 28. Bearings and 32 hold the turntable axle 28 so the turntable 14 will rotate free of wobble and without run-out. A worm gear 34 attached to the turntable axle 28, and driven by a worm 36, causes the turntable 14 to revolve. A motor 37 provides the torque to turn the worm 36. The turntable axle 28 extends below the lower bearing 32.

The uppermost surface of the turntable 14 has a means for attaching the work piece 16 to it. The means is a plurality of small dog clamps 38. Alternative clamping means to hold the work piece 16 on the turntable 14 include: a magnetic chuck; a vacuum chuck; adhesives; or any. other suitable device.

The work piece 16 to be ruled with a plurality of grooves to create a master die is brass though other metals and materials are suitable.

The cutting head 18 positions the cutting tool 20 over the work piece 16. The elements and arrangement comprising the cutting head 18 can be best understood by general reference to FIGS. 1, 2, 2a, and 4. The dimensions of the cutting head 18 and the orientation of its components are such that the cutting tool 20 will track in and out along a diameter through the rotational center of the turntable 14. The cutting head 18 incorporates three principal degrees of freedom for the cutting tool 20: elevation; radial position; and rotation about a horizontal axis.

Rotational freedom is achieved by a special low friction arcuate bearing 40 that supports a cutting tool holder 42. The lower portion of the cutting tool holder 42 has a tool chuck 44 by means of which the cutting tool 20 is releasably held. The tool chuck 44 permits removing the cutting tool 20 for sharpening or replacement and the substitution of other cutting tools with cutting edges of different shape as desired.

FIGS. 1 and 2a best show the general configuration of the low friction arcuate bearing 40. FIG. 2a shows the arrangement of parts in perspective and separated for clarity. The arcuate bearing 40 comprises arcuate journal surfaces 46a and 46b and arcuate bearing surfaces 48a and 48b. They are all concentric about a selected point located along the cutting edge of the tool 20, usually at its tip.

The two concentric arcuate journal surfaces 46a and 46b are formed on a journal section 50 to which the cutting tool holder 42 is joined. The journal surfaces 46a and 46b slide in a bearing section 52 comprising the two arcuate bearing surfaces 48a and 48b. To retain the cutting tool holder 42 firmly and without any axial play or general looseness, the arcuate bearing and journal surfaces 46a, 46b, 48a, and 48b are each configured as a circumferential section of a frustum and used in conjunction with planar sliding surfaces 52a and 52b. All the foregoing surfaces fit closely together and are lubricated to reduce the friction between them. The foregoing arrangement can be considered as a dovetail machine slide in arcuate form to provide rotation about a point laterally displaced from the bearing 40. Hydrostatic or pneumatic support can be usefully incorpo rated at the mating surfaces of the arcuate bearing 40 to reduce friction to a minimum.

The cutting tool holder 42 has a lever arm 54 attached to it. The lever arm 54 extends to the pitch control mechanism 22 where it rests on the cam 26. The pitch of the cutting tool 20 is controlled by means of the pitch control mechanism 22 raising the lowering the lever arm 54 as explained below.

The concentric bearing surfaces 46a and 46b and the planar sliding surface 52b are formed in a vertical slide 56 that supports the tool holder 42 through the arcuate journal 50. The vertical slide includes a male dovetail slider 58 that slides through a female dovetail slideway 60. The female dovetail slideway 60 is formed in a horizontal slide 62. An arm 64 extends upwardly from the horizontal slider 62 and projects an extension 66 outwardly over the vertical slider 56. A vertical lead screw 68 is rotatably fitted into a hole tapped through the extension 66. The lower end of the vertical lead screw 68 fits into a hold in the upper part of the vertical slide 56. A retainer means 70 connects the lead screw 68 to the vertical slide 56 so the former can rotate inside the latter but that they cannot separate. At the upper end of the lead screw 68 is a hand wheel 72 for rotating it. One will now understand that rotating the hand wheel 72 changes the vertical slide 56s elevation. The foregoing arrangement provides the means by which the tool 20s depth of cut is set and also the means for raising the tool 20 above the work piece 16 so it can be moved to the location of another groove without marring the work piece 16. All the parts described for operating the vertical slide 56 are made and fitted together with the accuracy and sturdiness required for constructing a proper ruling engine 10. This construction standard applies to all the elements of the ruling engine 10.

By supporting the vertical slide 56, the horizontal slide 62 provides the third degree of freedom to the tool 20. It is the guide element for the radial positioning mechanism. The horizontal slide 62 has a female dovetail slideway 74 that engages and slides along a male dovetail slide 76 that is joined to a pedestal 78 projecting upwardly from the frame 12. Reference should be had to FIGS. 1, 2, and 4 for a better appreciation of the arrangement and relation of the parts comprising the radial positioning mechanism. A pair of arms 80 and 02 extend forward from the top of the pedestal 70. They each contain a plain bearing 84 and 06, respectively, arranged to support a horizontal lead screw so it can rotate but not so it can move axially. A hand wheel 90 is attached to the end of the horizontal lead screw 08 extending through the plain bearing 84.

The horizontal lead screw 88 passes through and movably engages a threaded hole in the arm 64 that extends upwardly from the horizontal slide 62. Rotating the horizontal lead screw 88 will result in relative axial movement between it and the arm 64. Since the plain bearings 84 and 86 prevent axial movement of the horizontal lead screw 88, the horizontal slide 62 will move. It will slide along the male dovetail slide 76 guided by its female dovetail slideway 74. Thus, rotating the hand wheel 90 causes the tool 20 to move along a diameter of the turntable 14. It provides the means by which an operator can adjust the ruling engine to rule an echelon of a specific radius.

If the ruling engine 10 is set so the contact surface is parallel to the movement direction of the horizontal slide 62, no changes in the cutting tool s pitch will result. However, if the contact surface is not parallel to the movement of the horizontal slide 62, a slight change in pitch will result. The change in pitch due to radial movement of the cutting tool 20 can be used to affect, at least in part, changes in pitch as a function of the tool 20s radius from the center of rotation of the turntable 14. However, the operation of the ruling engine 10 will be easier to understand if it is assumed that the pitch control mechanism 22 is moved a distance equal to the movement of the horizontal slide 62 so as to restore the distance between the contact point and the pivot point.

Reference should now be had to FIGS. 1, 3, and 4 to gain a fuller understanding of the pitch control mechanism 22 and how it may be used to control the pitch of the cutting tool 20 as a function of the tool 205 radial distance from the work piece 16s center of rotation and as a function of its azimuth relative to the revolving work piece 16. n

The pitch control mechanism 22 comprises a carriage adapted for sliding longitudinally along a pair of inverted vee rails 102 and 104. The rails 102 and 104 are formed a part of the rigid frame 12. To move the carriage 100 longitudinally, a longitudinal lead screw 106 is provided. An internally threaded collar 100 underslung from the carriage 100 engages the longitudinal lead screw 106. The ends of the longitudinal lead screw 106 are supported in plain bearings 110 (only the outward one is shown) that prevent it from moving axially. Therefore, rotation of the longitudinal lead screw 106 causes the carriage 100 to move instead because of their engagement through the collar 108. A hand wheel 112 attached to the outer end of the longitudinal lead screw 106 provides a convenient means by which the operator can rotate the longitudinal lead screw 106 and adjust the longitudinal position of the carriage 100. The distance and direction the carriage 100 moves is proportional to the number of degrees clockwise or counterclockwise through which the hand wheel 112 rotates the longitudinal lead screw 106.

A vertical column 114 extends upwardly from the carriage 100. It has a female dovetail slideway 116 machined into its front. The vertical column 114 guidingly supports a cam carriage 120 by means of a male dovetail slide 118, attached to the cam carriage 120, slideably engaged with its female dovetail slideway 116. An elevation lead screw 122, threaded through a tapped hole 124 in an arm 126 extending from the vertical column 114 over the dovetail slideway 116, engages the cam carriage 120 by means of a retainer 128. The retainer 128 permits the elevation lead screw 122 to rotate relative to the cam carriage but not to separate therefrom. Rotation of the elevation lead screw 122 causes it to move in an axial direction through the tapped hole 124 in the arm 126 of the vertical column 114. it moves the cam carriage 120 accordingly.

An elevation hand wheel 130 attached to the upper end of the elevation lead screw 122 provides a convenient means by which the operator can rotate the elevation lead screw 122 and thereby adjust the elevation of the cam carriage 120. The distance the cam carriage 120 moves up or down is proportional to the number of degrees clockwise or counterclockwise the hand wheel 130 rotates the elevation lead screw 122.

The cam carriage 120 has two bearings 132 and 134 supporting a cam shaft 136. The cam shaft 136 projects beyond the cam carriage 120. The cam 26 is attached to the cam shaft 136 and it supports the lever arm 54 that manipulates the tool holder 42 in its arcuate bearing 40 to set the pitch of the cutting tool 20. A bevel gear 138 is keyed to the cam shaft 136 so it will cause the cam 26 to turn synchronously with the turntable by means of the transmission 24 described below. Rotation of the cam 26 raises and lowers the lever arm 54 according to the shape of the cam 26.

The means for causing the cam 26 to rotate synchronously with the turntable 114 is the transmission 24. It is best understood by reference to FIGS. 1, 3, and 4.

The transmission 24 is built so the cam 26 will rotate 2 for each 1 the turntable 14 rotates. Because of the bi-fold symmetry of most anamorphic Fresnel optical elements, the same cam shape that controls the pitch between the 0 azimuth and the 180 azimuth can control the pitch from the 180 azimuth to the 360 azimuth. For Fresnel optics lacking bi-fold symmetry, the transmission 24 can be changed in a conventional way so the cam 26 will rotate 1 for each degree the turntable rotates.

A bevel gear 150, keyed to the lower end of the turntable axle 20, engages a bevel gear 152 half its size. The size ratio between them effects a 2-to-l speed increase so the cam 26 will rotate 2 for each degree the turntable 14 rotates. The bevel gear 152 is keyed to a long horizontal splined shaft 154 extending the length of the vee rails 102 and 103. Two bearings 156 and 158 rotatably support the splined shaft 154 near its ends.

An internally splined bevel gear 160 is fitted to the splined shaft 154 so it can slide axially along the splined shaft 154. They rotate together because of the mutual engagement between their respective splines. The internally splined bevel gear 160 is held by a ball bearing 162 retained in a casing 164 underslung from the carriage 100. It should be clear, especially from FIG. 1, that longitudinal movement of the carriage 100, caused by the longitudinal lead screw 106, will slide the internally splined bevel gear 160 along the splined shaft 154 short vertical spline shaft 166 and rotatably supported by a ball bearing 168. The vertical spline 166 extends up, inside the cam carriage 120. A second internally splined bevel gear 170 is fitted to the vertical splined shaft 166 so it can slide axially along the vertical splined shaft 166. The second splined bevel gear 170 and the vertical splined shaft 166 rotate together because of the mutual engagement between their respective splines. The second splined bevel gear 170 is held by a ball bearing 172 retained at the lower wall of the,

cam carriage 120. It should be clear, especially from FIG. 3, that vertical movement of the cam carriage 120, caused by rotating the elevation lead screw 122, will slide the second internally splined bevel gear 170 along the vertical splined shaft 166 without inhibiting its rotation therewith. The ball bearing 172 and the bevel gear 1 70 help maintain the alignment of the vertical splined shaft 166 by their close fit with the shaft 166s free end.

The second splined bevel gear 170 engages and rotates the bevel gear 138 keyed to the cam shaft 136. One will now perceive how the transmission 24 rotates the cam 26 synchronously with the turntable 14 without regard to the longitudinal position of the cam 26 or its elevation.

Consider a groove to be ruled at a mean radius on the work piece 16 with an anamorphic face on the ruling. The face will have a minimum pitch at 2 azimuths 180 apart and a maximum pitch at two other azimuths 180 apart from each other and 90 from the first 2 azimuths. Generally, the anamorphic facets will have mirror symmetry about a diameter through both pairs of azimuths, and that will be assumed herein.

Consider further that the longitudinal position of the carriage 100 and the elevation of the cam carriage 120 are temporarily fixed. The effective length of the lever arm 54, i.e., the distance between the tool 20s point and the point of contact between the cam 26 and the lever arm 54, is known and fixed. It is assumed that the pivot point ofthe arcuate bearing 40 coincides with the point of the tool 20.

From the design of the anamorphic Fresnel optic for which a master die is being ruled, one knows the maximum and minimum pitch of each facet. One also knows how the pitch changes between the maximum and minimum as a function of azimuth. For the purposes of this explanation, the anamorphic Fresnel optic is chosen to be a mirror combining a component of positive spherical refracting power and a component of positive cylindrical power, the latter being oriented so as to have no power at the azimuth and at the- 180 azimuth.

A positive spherical power Fresnel lens mirror comprises a plurality of concentric rulings whose pitch is a minimum at the center and increases as a function of radius. (See FIG. a.) Superimposing the component of positive cylindrical power thereon has no effect on the pitch of the facets along a first (0, 180) diameter through the rulings; however, it increases the pitch of each facet along a second (90, 270) diameter, orthogonal to the first diameter, by a calculatable amount.

(See FIG. 5b.) The difference in the pitches of each facet increases with the radius of the facet.

To produce the anamorphic Fresnel mirror shown in FIG. 5b, the cam surface 140 must have a shape that will raise the lever arm 54 a predetermined distance as the turntable 14 rotates a first 90 and that will lower the lever arm 54 the same amount as the turntable rotates the next Because of the bi-fold symmetry in the design of anamorphic Fresnel mirror of FIG. 5, the cam 26 can have a single lobe (rise and fall) and rotate twice for each revolution of the turntable 14.

The shape of the cam surface 140 is fixed. The pitch change it causes between the 0 and 90 azimuths of the work piece 16 is a function of its rise and of the distance between the contact point and the tool 20s point. It follows that the pitch change due to the fixed cam surface 140 can be changed by changing that distance.

A specific cam surface 140 for ruling an anamorphic facet of radius R will provide a satisfactory approximation of the cam surface required to rule anamorphic facets adjacent to the one of radius R. Indeed, it will suffice to rule all the facets with radii between R AR and R AR for a particular anamorphic Fresnel optic. The size of AR depends on the accuracy desired of the anamorphic Fresnel optic.

If the cam 26 and movement of the carriage cannot completely provide the required range of pitch control for the inner and outermost rulings as a function of the work piece l6s azimuth, then additional cams of different design can be used.

Either or both a longitudinal movement of the carriage 100 and/or an elevational movement of the cam carriage will change the lowest position the lever arm 54 can assume and thereby change the minimum pitch of the cutting tool 20-will attain as the turntable 14 and the cam 26 rotate synchronously through means of the transmission 24. As the ruling engine 10 is ad justed to rule successively larger diameter grooves (echelons) on the anamorphic Fresnel mirror of FIG. 5b, the minimum and maximum pitch angles achieved by the cutting tool 20 must be changed in accord with the anamorphic optical design. The operator can do this by changing the elevation of the cam carriage 120 or the distance between the tool 20s point and the contact point between the cam 26 and the lever arm 54 or by doing both. Increasing the elevation or decreasing the longitudinal distance increases the tool 20s pitch. Consideration should be given to the effect on the pitch change of the non-radial path along which the cam 26 tracks as its longitudinal position changes.

THE METHOD FOR RULING AN ANAMORPHIC FRESNEL OPTIC The first step in making a master die for molding an anamorphic Fresnel optical element is to determine its optical design. In the case of an anamorphic Fresnel optical element like the one described in my said US. Pat. No. 3,735,685, one might begin the design by choosing how closely to rule the echelons, i.e., the number of echelons per centimeter; then for each echelon determine the pitch of the facet at as many different azimuths as necessary to provide an accurate idea of how the pitch, for each echelon, changes as a function of azimuth. With the foregoing knowledge, a cam 26 can be made to guide the cutting tool 20 while it accurately cuts a specific anamorphic echelon on the work piece 16. It will be understood that the cam design is for a specific setting of the pitch control mechanism 22s elevational and longitudinal controls. The echelons adjacent to the specific anamorphic echelon the cam 26 is design for can be cut with the same cam 26 by resetting the elevation and longitude of the cam shaft 136 as required. The cam 26 designed for a specams for those echelons too far removed from the one the cam is intended for must be designed and used if the approximation is not sufficiently accurate.

In practice, the settings of the control hand wheels on the ruling engine 10 and the choice of cams is provided to the operator of the ruling engine 10 as a tabulation listing the cam choice and the settings of the hand wheels 90, 72, 112 and 130. They are, respectively, the radial location and final depth of cut of the cutting tool and the longitude and elevation of the cam shaft 136. The tabulation might also specify cutting tool 20s shape if more than one shape tool is used.

The operator of the ruling engine 10 attaches the work piece 16 to the turntable 14 by means of the clamps38. Referring to his tabulation, the operator determines the settings of the hand wheels 90, 112, and 130. After ascertaining that the tool 20 will not touch the work piece, he adjusts the hand wheels 90, 112, and 1330 indicated to rule a first echelon on the work piece 16. This sets the radial distance of the cutting tool 20 from the turntable 14s center of rotation, sets the cam shaft l36s elevation and longitudinal distance from the cutting tool 20. The operator then attaches the proper cam 26, as indicated by the tabulation, to the cam shaft 136 and changes the tool 20 if indicated by his tabulation. The sequence of the foregoing steps can be altered for convenience.

After making the foregoing settings of the ruling engine 10, the operator starts the motor 37. As the turntable l4 and the cam 26 begin rotating, the operator uses the hand wheel 72 to engage the cutting tool 20 with the work piece 16. He rotates the hand wheel 72 until it reaches the setting indicated by the tabulation. The cutting tool 20 thereby rules an echelon with the proper depth. After allowing the work piece 16 to rotate several times with the cutting tool 20 at the final depth to clean up the echelon and provide it with a smooth facet, he raises the cutting tool 20 to clear the work piece 16.

To rule the adjacent echelon, the operator refers to the tabulation again and resets the horizontal slide 62 that determines the radius of each echelon by rotating the hand wheel 90. He also resets the other hand wheels according to the data in the tabulation. The tool 20 is advanced to the depth of cut by resetting the hand wheel 130 as indicated by the tabulation. The turntable 14 and the other parts of the ruling engine 10 driven by the motor 37 have continued to rotate. These steps are repeated, as required, to rule an entire master die for molding an anamorphic Fresnel lens. As noted above, it might be necessary at some point in the repetitive sequence of operations to change the cam 26 and/or the cutting tool 20.

The structure of the ruling engine 10 provides an essential step in the processes of ruling the master die, that of changing the tilt of the cutting tool 20 between a predetermined maximum pitch and a predetermined minimum pitch as a function of the cutting tool 20s azimuth relative to the rotating workpiece 16.

Multiple copies of the anamorphic Fresnel optic can be made from the master die generated according to the preceding description by the methods developed for copying conventional Fresnel optics. Those skilled in the art know the ruling engine can generate an ana- W morphic Fresnel optical element directly as well as the die for molding it.

For the purposes of clarity, the structure and functioning of the ruling engine 10 have been kept simple. It should be understood that the present invention contemplates applying electrical or mechanical means for automatically performing steps described as manual operations, including the storage in mechanical or electrical memories of the tabulated information and means for retrieving the information from storage and using it to control the automatic means incorporated into the ruling engine 10. It also contemplates a more complex mechanism to enable the machine to rule el' liptical echelons, as well as circular echelons, whose pitch varies as a function of azimuth. Elliptical echelons could be generated by modifying the turntable 14 to reciprocate transverse to its axis as a function of its rotation.

Since certain changes may be made in the above apparatus and method without departing from the scope of the invention herein involved, it is intended that all matter contained in the above description or shown in the accompanying drawings shall be interpreted as illustrative and not in a limiting sense.

What is claimed is:

1. Apparatus comprising:

means for mounting a cutting tool;

means for mounting a work piece having a substantially flat work surface in operative relation with said cutting tool;

means for effecting relative motion between said work piece and said cutting tool;

first means for automatically varying the cutting angle of said cutting tool with respect to said work piece responsive to said relative motion to cause said cutting tool to generate an anamorphic shaped groove in said work piece;

second means for varying said cutting angle independent of said first means; and

third means for varying said cutting angle independent of said first and second means.

2. The apparatus of claim 1, additionally including means for adjusting thelocation of said cutting tool with respect to said work piece prior to effecting said relative motion and means for adjusting the initial angular orientation of said cutting tool with respect to said work piece prior to effecting said relative motion so that a plurality of spaced apart grooves may be generated in said work piece with each successive said anamorphic groove being canted, relative to a preceding said anamorphic groove, uniformly along their length.

3. An apparatus, comprising:

means for mounting a cutting tool;

means for mounting a work piece with a flat work surface in operative relation with said cutting tool; first adjusting means for adjusting the cutting angle of said cutting tool with respect to said work piece; second adjusting means for adjusting the cutting angle of said cutting tool with respect to said work piece independent of said first adjusting means; means for effecting relative motion between said cutting tool and said work surface in two coordinates; first means for controlling said cutting angle as a predetermined function of said cutting tools location on said work surface in the first coordinate; and

second means for controlling said cutting angle as a predetermined function of said cutting tools location on said work surface in the second coordinate so said apparatus can generate a die for molding said cutting tool on said work surface relative to a reference direction from the work surfaces rotational axis.

5. The apparatus described in claim 4, wherein said second controlling means includes a cam rotationally slaved to said relative motion effecting means and said first and second adjusting means include means for varying the distance between said cams axis of rotation and said cutting tool in different directions,

6. In an apparatus useful for ruling a die for molding an axially symmetric echelon optical element including: means for holding a work piece having a work surface; means for rotating said work piece about an axis normal to the center of its work surface; means for holding acutting tool; means for positioning said cutting tool along a radius from said axis; and means for causing said cutting tool to groove said work surface;

12 the improvement comprising:

a. first adjusting means for adjusting the pitch angle between said cutting tool and said axis;

second adjusting means for adjusting the pitch angle between said cutting tool and said axis independent of said first adjusting means;

c. means for determining the azimuth of said cutting tool relative to a reference direction on said work surface as said work surface rotates; I

(1. means for controlling said pitch angle as a predetermined function of said radius; and

e. means for controlling said pitch angle as a predetermined function of said azimuth while said work surface rotates so a resulting echelon optical element will be anamorphic rather than axially symmetric.

7. The improved apparatus described in claim 6, further including rotatable cam means and wherein said first adjusting means includes means for adjusting the distance between said cam means and said cutting tool in a first direction and said second adjusting means includes means for adjusting the distance between said cam means and said cutting tool in a different directlon. 

1. Apparatus comprising: means for mounting a cutting tool; means for mounting a work piece having a substantially flat work surface in operative relation with said cutting tool; means for effecting relative motion between said work piece and said cutting tool; first means for automatically varying the cutting angle of said cutting tool with respect to said work piece responsive to said relative motion to cause said cutting tool to generate an anamorphic shaped groove in said work piece; second means for varying said cutting angle independent of said first means; and third means for varying said cutting angle independent of said first and second means.
 2. The apparatus of claim 1, additionally including means for adjusting the location of said cutting tool with respect to said work piece prior to effecting said relative motion and means for adjusting the initial angular orientation of said cutting tool with respect to said work piece prior to effecting said relative motion so that a plurality of spaced apart grooves may be generated in said work piece with each successive said anamorphic groove being canted, relative to a preceding said anamorphic groove, uniformly along their length.
 3. An apparatus, comprising: means for mounting a cutting tool; means for mounting a work piece with a flat work surface in operative relation with said cutting tool; first adjusting means for adjusting the cutting angle of said cutting tool with respect to said work piece; second adjusting means for adjusting the cutting angle of said cutting tool with respect to said work piece independent of said first adjusting means; means for effecting relative motion between said cutting tool and said work surface in two coordinates; first means for controlling said cutting angle as a predetermined function of said cutting tool''s location on said work surface in the fiRst coordinate; and second means for controlling said cutting angle as a predetermined function of said cutting tool''s location on said work surface in the second coordinate so said apparatus can generate a die for molding anamorphic Fresnel optical elements.
 4. The apparatus described in claim 3, wherein said relative motion between said cutting tool and said work surface is rotational, said coordinates being the radial distance of said cutting tool along said work surface from the center of rotation and the angular position of said cutting tool on said work surface relative to a reference direction from the work surface''s rotational axis.
 5. The apparatus described in claim 4, wherein said second controlling means includes a cam rotationally slaved to said relative motion effecting means and said first and second adjusting means include means for varying the distance between said cam''s axis of rotation and said cutting tool in different directions.
 6. In an apparatus useful for ruling a die for molding an axially symmetric echelon optical element including: means for holding a work piece having a work surface; means for rotating said work piece about an axis normal to the center of its work surface; means for holding a cutting tool; means for positioning said cutting tool along a radius from said axis; and means for causing said cutting tool to groove said work surface; the improvement comprising: a. first adjusting means for adjusting the pitch angle between said cutting tool and said axis; second adjusting means for adjusting the pitch angle between said cutting tool and said axis independent of said first adjusting means; c. means for determining the azimuth of said cutting tool relative to a reference direction on said work surface as said work surface rotates; d. means for controlling said pitch angle as a predetermined function of said radius; and e. means for controlling said pitch angle as a predetermined function of said azimuth while said work surface rotates so a resulting echelon optical element will be anamorphic rather than axially symmetric.
 7. The improved apparatus described in claim 6, further including rotatable cam means and wherein said first adjusting means includes means for adjusting the distance between said cam means and said cutting tool in a first direction and said second adjusting means includes means for adjusting the distance between said cam means and said cutting tool in a different direction. 